ROLE OF YIELD-TO-TENSILE STRENGTH RATIO IN THE DESIGN OF STEEL STRUCTURES K.S.Sivakumaran Professor, Department of Civil Engineering, McMaster University, Hamilton, Ontario, L8S 4L7, CANADA Keywords: Bending Moment, Elastic Design, Seismic, Specifications, Stress-Strain, Y/T Ratio Abstract Avoidance of structural collapse during extreme events like earthquakes relies on the available ductility of the structure and its members and components. Over the years, the yield stress-to- tensile strength ratio (Y/T), which is a measure of the ductility of steel, has increased from 0.5 to 0.85 or more. This paper discusses; (a) Yield stress-tensile strength- Y/T ratio relations, (b) relevance of Y/T ratio in structural design and (c) treatment of Y/T ratio in the North American steel design codes. The focus of this paper is limited to ductility aspects of civil engineering structural designs, such as design of buildings and bridges. Statistical analysis of mechanical properties of steels shows that the Y/T ratio increases with increasing yield stress, and with increasing tensile strengths of steel. However, Y/T ratio is significant only in steel structural systems and members that are expected to withstand strain-hardening range stresses and strains, such as ductile elements of earthquake resistant structural systems, stress concentration situations like holes in tension members and beams, and structures designed based on plastic analysis. This paper discusses the required geometric and material conditions to prevent premature failures of steel members and structures and to ensure adequate ductility. Introduction Design of structures to withstand nature’s fury, such earthquakes, hurricanes, tornados, snowstorm, etc., has been a challenge and at times had been a failure. Understanding the nature and the impact of such natural hazards and understanding the use and occupancy requirements of a structure are essential in order to achieve a successful structural design. As a minimum, structures are designed to be safe and serviceable during normal use and occupancy and protected from collapse during extreme events like earthquakes. Safety is assured provided the structures and their members are designed to have sufficient strength and stability such that the factored resistance is greater or equal to the effects of factored loads acting in the most critical combination. Furthermore, configuration of the structural members and their connections must ensure resistance to widespread collapse as a consequence of local failure (sufficient structural integrity). Serviceability is assured by proportioning the structural members and frames such that the serviceability parameters (deflection, vibration, etc.) are within acceptable limits for the nature of the materials supported and for the intended use and occupancy. In order to maximize the economical efficiency of structures, prevention of collapse during extreme events like earthquakes relies on the ductility of the structure. “Ductility” is the ability of the structure, its members and elements, and the structural material to undergo inelastic deformations without 63 loosing its strength. Structural steel is the most ductile of the modern structural engineering materials. In Canada, the structural steel must meet the requirements of CSA standard G40.20/G40.21 (CSA, 2004), whereas in U.S.A. they must meet the requirements of the American Society for Testing and Materials standard (ASTM, 2008). Early twentieth century North American buildings and bridges used mild-carbon structural steel with a specified minimum yield stress Fy of 190 MPa - 225 MPa. Corresponding tensile strength Fu was 380 MPa – 450 MPa, giving a specified yield-to-tensile strength ratio Fy/F u of 0.5. The yield-to-tensile ratio (Y/T) is a measure of strain hardening ability and the ductility of steel. The improvements in steel making technologies over the years, motivated by the desire to use higher strength structural steels, have made possible to produce higher strength steels (345 MPa to 690 MPa yield strength) with improved weldability, high toughness, and improved atmospheric corrosion resistance (weathering). Currently, the steel grade ASTM A992/A992M has become the dominant material specification for wide flange shapes in U.S.A. and in Canada. The ASTM A992 requirements for tensile properties include; yield point range of 345-450 MPa (50-65 ksi), minimum tensile strength of 450 MPa (65 ksi), and a maximum yield-to-tensile strength ratio of 0.85. Resulting F y/F u of A992 steel is between 0.77 and 0.85. In recent years A913/913M grade steels, which are high-strength low-alloy steel shapes of structural quality produced by a quenching and self-tempering process, have been introduced in the building codes. The ASTM A913 Grade 65 steel mechanical properties requirements are yield strength 450 MPa (65 ksi), and tensile strength of 550 MPa, resulting in a Fy/F u ratio of 0.82. Steels for application in bridges are covered in ASTM A709/709M. High-performance steels (HPS) are the newest additions to the family of bridge steels. The HPS-70W [485W], which has been used the most, has ASTM requirements of minimum yield strength 485 MPa (70 ksi), and tensile strength of 585-760 MPa, resulting in a F y/F u ratio of 0.83 – 0.64. HPS-100W [690W], with yield strength 690 MPa (100 ksi), and tensile strength of 760-895 MPa which gives a F y/F u ratio of 0.91 – 0.77, is also available to reduce thickness of bridge members (Brockenbrough and Merritt, 2006). Therefore, over the years the yield-to-tensile strength ratio of structural steel has increased from 0.5 to a code permitted maximum of 0.85. Higher Y/T ratio may imply lesser strain hardening ability and lesser material ductility. Concern has been expressed over the high Y/T ratio of high strength steels ability to provide adequate strain hardening and ductility to achieve sufficient safety margins against fracture, somewhat comparable to the safety margins associated with low Y/T ratio steels. This paper discusses (a) Yield stress-Tensile strength-Y/T ratio relations, (b) role of Y/T ratio in structural design and (c) treatment of Y/T ratio in current North American steel design codes. The focus of this paper is limited to ductility aspects of civil engineering structural designs, such as ductile design of steel buildings and inelastic design of steel bridges. 64 Stress-Strain Properties of Structural Steel Stress-strain relations are the most commonly used mechanical properties of material in civil engineering structural design. Such properties of steel are established through tension tests in accordance with ASTM A370 testing procedures “Standard Test Methods and Definitions for Mechanical Testing of Steel Products”, (ASTM, 2008). The mechanical properties of interest in a civil engineering structural design are; yield stress (F y), yield strain ( εy), tensile strength (F u), ultimate strain ( εu), and perhaps the fracture strain ( εf). Often it is convenient to use the 0.2% off- set method to establish the yield stress and strain, though stress at yield plateau may be used to identify such values for steels exhibiting yield plateau. Recent experiments (Arasaratnam, 2008), on identical tensile coupons from A992 steel grade show an average yield stress and strain of 445 MPa, and 0.0022, respectively, and the tensile strength and the ultimate strain of 577 MPa, and 0.1381, respectively. The strain at fracture ( εf), based on 200 mm (8”) gauge extensometer measurements was 0.2082. These values compared well with the mill test report given by the supplier of these steel beams. Figure 1 shows the idealized stress-strain properties of the steel. From the yield and ultimate stress and strain, other salient parameters such as elastic modulus (E), strain hardening modulus (E st ), yield ratio (Y/T) yield stress/tensile strength, elongation capacity reflected through ductility ratio (µ) ultimate strain/yield strain, etc. can be derived. Based on test results E = 200,900 MPa, E st = 971 MPa, Y/T = 0.77, and µ = 63 were obtained. Yield Stress, Tensile Strength and Yield-to-Tensile Strength Ratio Relations Prior to the introduction of probability based design of steel structures in the 1970’s, statistical values for mechanical properties were not generally established because the steel specifications of that era worked with specified minimum values. The studies by Galambos and Ravindra (1978) and by Kennedy and Gad Aly (1980), which established the statistical parameters for steel design for the American and Canadian steel design standards, respectively, focussed on the yield stress and not the ultimate strength. Even the steel related research studies of that era reported either incomplete or limited material property data related to the steels used in their research. Lilly and Carpenter (1940), however, provided the yield point and tensile strength of web plate, cover plates, and flange angles used in their investigation related to riveted plate girders. Two tension coupons each were considered for each of these elements, and the yield stress ranged 290-370 MPa(42-54 ksi) and the corresponding tensile strength ranged 419-505 MPa(61-73 ksi). Since then, however, various studies have reported on the statistical yield stress Figure 1. Idealized stress-strain properties 65 and the corresponding tensile strength of different steel grades; • Yamanouchi, et. al. (1990) established the statistical features of mechanical properties of SS41 (Specified minimum F y = 235 MPa, and F u = 403-510 MPa) and SM50A (Specified minimum F y = 315 MPa, and F u = 490-607 MPa) steel grades, since these grades were widely used at that time for general steel building structures in Japan. This study was based on 4160 mill test reports of these grades of steel that were produced with blast furnaces at six major Japanese mills during the last six months of 1986. The study observed that, for the same steel grade, the measured yield stress is higher in thin plates than thick plates.